BOSTON — David Ortiz remembers visiting Fenway Park with Minnesota and seeing empty seats.

"The only sellout was when Pedro was pitching," he said. "Otherwise, it was a regular crowd."

Pedro Martinez is long gone from the Boston Red Sox, but the sellout streak that started in a game he pitched figures to continue for a long time.

Boston's regular-season sellout streak, which began on May 15, 2003, is slated to reach a major league record 456 when the Red Sox host Tampa Bay on Monday night. On Wednesday, the Red Sox tied the record set by the Cleveland Indians at Jacobs Field from June 12, 1995, to April 2, 2001, a run that ended on a 42-degree day with a 7-4 loss to the Chicago White Sox.

Fenway Park has the fewest seats in the major leagues, with a capacity of 37,400 for night games and 36,984 for day games. During the streak, 16,298,532 fans streamed into Fenway.

Boston could sell many more tickets if it had the room. But with a desire to retain a cozy atmosphere and the shortage of space in which to expand in a city neighborhood, the Red Sox only plan to add about 200 seats next year.

Compare that with the huge economic boost their rival New York Yankees will get next season, when they open their new stadium, where the best seats sell for $500-$2,500.

"We generate a considerable amount of our revenue from gate receipts and concessions," team president Larry Lucchino said. "We call Fenway the little engine that could, and we think the Yankees are building this gigantic bullet train."

Ortiz joined the Red Sox in 2003 and had three hits in the game that began the streak, a 12-3 win over the Texas Rangers and Alex Rodriguez.

"I came to play here and we won and started to go to the World Series," Ortiz said, "and since (then) everything has changed. It's just crazy."

Fans like to see good teams. Cleveland won two AL pennants during its sellout streak. Boston has won two World Series since 2003.

Sean Casey, now with Boston, played six games for the Indians in September 1997.

"That was exciting when they were selling out so much," he said. "The cool thing is I've played around in enough places to know this doesn't happen everywhere."

So how did it happen in Boston?

When John Henry's ownership group took over the team in February 2002, it inherited passionate fans and a unique ballpark that opened in 1912 but had been neglected while the previous owners focused on trying to build a new stadium.

Henry's group decided to keep Fenway Park — and improve it. Seats were built above the Green Monster in left field, on top of the right field roof and in foul territory at field level from first to third base.

Concourses were added, allowing fans to leave their narrow seats to stretch their legs — and spectators put more money in the team's coffers by patronizing the increased number of concession stands.

"The comforts of Fenway and the desirability of Fenway, its urban roots, make it a special place," chief operating officer Mike Dee said. "We sold out every game in September of 2006 at a time where we had fallen out of contention."

Boston's 48-19 home record is the best in the majors. The Red Sox appear energized by their fans.

"To be able to come home from a road trip and play in front of a sellout crowd every night is pretty special," said pitcher Tim Wakefield, one of four players with the Red Sox throughout the streak. "Not a lot of people get a chance to do that."

There is a downside. Fans who want to see their favorite team at Fenway are shut out.

"I think it's just a beautiful park," said Jim Currie, a 55-year-old from Amesbury who was at the record-tying game Wednesday, a 5-4 win over Baltimore. "I feel like a kid again. But I wish they wouldn't sell out every game. I haven't been here in about five years."

Some fans travel to Baltimore or Toronto to see the Red Sox. Some line up on the day of the game, when the team puts several hundred tickets on sale.

The team sells 21,000 seats as season tickets and begins selling tickets for games in April and May in early December, a month earlier than it once did.

"It's certainly something that we wish we could rectify, that every fan who wanted to buy a ticket could buy one," Dee said. "The consolation here is we've taken a lot of steps to make sure tickets are distributed in a fair and equitable way, like random drawings for Monster seats."

The Red Sox have drawn 2,484,949 fans to 67 home games, an average of 37,646. Because the team sells standing room tickets, its attendance actually is 104.1 percent of its official seating capacity.

"The fans embrace this team, this organization, this place," Casey said. "Fenway Park brings something different than any other place in the league."

Back when he was with the Twins, Ortiz hit a long fly ball to right field at Fenway. Darren Bragg stretched over the fence and caught it — reaching into empty seats, with no fans to get in his way.

"If there were people on the other side, he wouldn't even have tried," Ortiz said with a chuckle.

That's hasn't been a problem for more than five years.

"Everything ends at some point," Lucchino said. "I'm sure the Indians were wondering when their streak would end, and it's inevitable that ours will end at some point. We just are counting on our fans to keep it going."